Synchronization and Chaotic Dynamics of A Josephson Junction Shunted by ‎A Negative Conductance

  • Authors

    • G. F. Pomalegni École de Génie Rural, Université Nationale d’Agriculture, Kétou, Bénin and Laboratoire de Mécanique des Fluides, de la Dynamique Nonlinéaire et de la Modélisation des ‎Systèmes Biologiques (LMFDNMSB); Institut de Mathématiques et de Sciences Physiques, ‎Porto-Novo, Bénin
    • M. A. Kakpo École Doctorale Sciences, Technologies, Ingénierie et Mathématiques (ED-STIM) ; Université ‎ Nationale des Sciences, Technologies, Ingénierie et Mathématiques (UNSTIM)‎ and Laboratoire de Mécanique des Fluides, de la Dynamique Nonlinéaire et de la Modélisation des ‎Systèmes Biologiques (LMFDNMSB); Institut de Mathématiques et de Sciences Physiques, ‎Porto-Novo, Bénin and Laboratoire de Physique et Applications (LPA) du Centre Universitaire de ‎Natitingou,Université Nationale des Sciences, Technologiques, Ingénierie et Mathématiques ‎‎(UNSTIM)Abomey, Bénin
    • C. H. Miwadinou École Doctorale Sciences, Technologies, Ingénierie et Mathématiques (ED-STIM) ; Université ‎ Nationale des Sciences, Technologies, Ingénierie et Mathématiques (UNSTIM)‎ and Laboratoire de Mécanique des Fluides, de la Dynamique Nonlinéaire et de la Modélisation des ‎Systèmes Biologiques (LMFDNMSB); Institut de Mathématiques et de Sciences Physiques, ‎Porto-Novo, Bénin and Laboratoire de Physique et Applications (LPA) du Centre Universitaire de ‎Natitingou,Université Nationale des Sciences, Technologiques, Ingénierie et Mathématiques ‎‎(UNSTIM)Abomey, Bénin and Département de Physique, Chimie et Technologie, École Normale Supérieure de ‎Natitingou, Université Nationale des Sciences, Technologiques, Ingénierie et Mathématiques ‎‎(UNSTIM) Abomey,Bénin
    https://doi.org/10.14419/z35t2r98

    Received date: July 11, 2025

    Accepted date: August 26, 2025

    Published date: October 9, 2025

  • Bifurcation and Chaos; Josephson Junction; Negative Conductance; Intermittency; ‎Synchronization

  • Abstract

    This paper presents a theoretical and numerical investigation of the RCLSJ model ‎‎(Resistively, Capacitively, and Inductively Shunted Junction), which is described by a ‎nonlinear current source characterized by the current-phase relationship ‎I_O (sin∅-α_1 sin2∅+α_2 sin3∅), coupled with a negative conductance. The rate ‎equations governing the RCLSJ model reveal that, depending on the parameter ‎regions, the system may either lack fixed points entirely or possess two or four fixed ‎points. These regions are determined by the intensity of the negative conductance ‎and the second-order harmonic term, under the assumption of a normalized critical ‎current. Our analysis demonstrates that the presence of negative conductance ‎suppresses certain hidden dynamical orders associated with periodic instabilities. ‎Furthermore, the introduction of the third-order harmonic term significantly alters ‎the nonlinear dynamics of the RCLSJ system. In addition, master-slave ‎synchronization studies indicate that the third-order harmonic modifies ‎synchronization frequencies by generating new resonance modes. For specific ‎threshold values of α2, it enhances synchronization, while variations in the intensity ‎of the negative conductance lead to higher-frequency oscillations. These different ‎influences induced by the negative conductance and the third-order harmonic term ‎of the junction suggest that the system could be used in the superconducting ‎circuits for qubits, synchronized oscillators for the generation of THz signals, and ‎also in computational neuroscience.

  • References

    1. Gu, X., Kockum, A. F., Miranowicz, A., Liu, Y., Nori, F.: Microwave photonics with superconducting quantum circuit. Physics Reports. 718-719 (2017). https://doi.org/10.1016/j.physrep.2017.10.002.
    2. Bunyk, P. I., et al.: Architectural considerations in the design of a superconducting quantum annealing processor. IEEE Transactions on Applied Superconductivity 24, (2014). https://doi.org/10.1109/TASC.2014.2318294.
    3. Hwang, S., et al.: Type-I superconductor pick-up coil in superconducting quantum interference device-based ultra-low field nuclear magnetic reso-nance. Applied Physics Letters. 104, 6 (2014). https://doi.org/10.1063/1.4865497.
    4. Belykh, V. N., Pedersen, N. F., Soerensen O. H.: Shunted Josephson junction model II. The nonautonomous case. Phys. Rev B. 16, 4860 (1977). https://doi.org/10.1103/PhysRevB.16.4860.
    5. Belykh, V. N., Pedersen, N. F., Soerensen O. H.: Shunted Josephson junction model I. The autonomous case. Phys. Rev B. 16, 4853 (1977). https://doi.org/10.1103/PhysRevB.16.4853.
    6. Crutchfield, J. P., Farmer, J. D., Huberman, B. A.: Properties of fully developed chaos in one-dimensional maps. Phys. Rep. 92(2), 45 (1982). https://doi.org/10.1016/0370-1573(82)90089-8.
    7. Likharev, K. K.: Dynamics of Josephson junctions and circuits. Springer, New York (1986).
    8. Dana, S. K., Sengupta D. C., Edoh, D. K.: Chaotic dynamics in Josephson junction. IEEE Trans. Circuit Syst. I 48, 990 (2001). https://doi.org/10.1109/81.940189.
    9. Whan, C.B., Cawthorne A. B, Lobb, C. J.:Synchronization and phase locking in two-dimensional arrays of Josephson junction. Phys. Rev. B. 53, 12340 ( 1996). https://doi.org/10.1103/PhysRevB.53.12340.
    10. Cawthorne A. B, Whan, C.B., Lobb, C. J: Complex dynamics of resistively and inductively shunted Josepson junction. J. Apll. Phys. 84,1126-1132 (1998). https://doi.org/10.1063/1.368113.
    11. Yang, X. S., Li, Q. Chaos Solitons Fractals 27, 25 (2006). https://doi.org/10.1016/j.chaos.2005.04.017.
    12. Wu, D. W., Liu, C. R. J. Eng. Ind. 107,107 (2014).
    13. Chen, D. Y., Zhao, W. L., Ma, X. Y., Zhang, R. F. Comput. Math Appl. 61, 3161 ( 2011). https://doi.org/10.1016/j.camwa.2011.04.010.
    14. Chen, D. Y., Zhang, R. F., Ma, X. Y., Liu, S. Nonlinear Dyn. 69, 35 (2011). https://doi.org/10.1007/s11071-011-0244-7.
    15. Chen, D. Y., Shi, L., Chen, H. T. Ma, X. Y. Nonlinear Dyn. 67, 1745 (2012). https://doi.org/10.1007/s11071-011-0102-7.
    16. Oseni, C. O. A., Monwanou, A. V.: Identical and reduced-order synchronization of some Josephson junction model. Eur. Phys. J. B. 95, 197 (2022). https://doi.org/10.1140/epjb/s10051-022-00462-2.
    17. Likharev, K. K.: Dynamics of Josephson junctions and circuits Gordon and breach. New York. 92.
    18. Ling, F. Y., Shen K.: Synchronization of chaos in resistive-capacitive-inductive shunted Josephson junctions. Chin. Phys. B 2 17, 550 (2008). https://doi.org/10.1088/1674-1056/17/2/033.
    19. Kakpo, M. A., Miwadinou, C. H.: Control of the chaotic dynamics of the RCLSJ model of the Josephson junction by the frequency of an excita-tion current and the internal resistance of a coil. Phys. Scr. 99, 085202 (2024). https://doi.org/10.1088/1402-4896/ad4ff0.
    20. Yokoi, M. et al.: Negative resistance state in superconducting NbSe2 induced by surface acoustic waves. SCIENCE ADVANCES.,6, 1377 (2020). https://doi.org/10.1126/sciadv.aba1377.
    21. Sergey, K. et al.: Band-selective third-harmonic generation in superconducting MgB2: Possible evidence for Higgs amplitude mode in the dirty limit . Phys. Rev. B 104, L140505 (2021).
    22. Seibold, G. et al.: Third-harmonic generation from collective modes in disordered superconductors. Phys. Rev. B 103, 014512 (2021). https://doi.org/10.1103/PhysRevB.103.014512.
    23. Pomalegni, G. F., Kakpo, M. A., Miwadinou, C. H.: Nonlinear dynamics and synchronization of an excited Josephson junction. J. Nonlinear Sci. Apll., 18, 225-238 (2025. https://doi.org/10.22436/jnsa.018.04.01.

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  • How to Cite

    Pomalegni, G. F. ., Kakpo, M. A. ., & Miwadinou, C. H. (2025). Synchronization and Chaotic Dynamics of A Josephson Junction Shunted by ‎A Negative Conductance. International Journal of Basic and Applied Sciences, 14(6), 169-181. https://doi.org/10.14419/z35t2r98